Two- and Three-Phase Flow Functions for
Numerical Simulation of EOR Processes
Amir Jahanbakhsh
BSc., MSc.
Submitted for the degree of Doctor of Philosophy
Petroleum Engineering
Heriot-Watt University
School of Energy, Geoscience, Infrastructure and Society
Institute of Petroleum Engineering
June 2016
The copyright in this thesis is owned by the author. Any quotation from the thesis or use of any of the information contained in it must acknowledge this thesis as the source of the quotation or information.
The understanding of governing mechanisms of multi-phase (oil, water, and gas) flow in porous media is of keen interest in petroleum and environmental engineering. In the petroleum engineering context, three-phase flow occurs in several important processes including in enhanced oil recovery (EOR). Recovery of a significant amount of the residual oil in reservoirs after primary recovery and secondary recovery (waterflooding) is important in order to tackle the increasing demand for the energy. EOR methods mainly involve two and three-phase flow in the reservoir. Relative permeability (kr) and
capillary pressure (Pc) are two important parameters in multiphase flow which describe
the interaction of each fluid in porous media. The importance of these flow functions will be even more significant for three-phase flow systems.
This thesis attempts to address three key issues.
(i) Improved determination of multi-phase flow functions (kr and Pc).
(ii) The impact of parameters affecting flow functions. (iii) Prediction of multi-phase flow functions.
Relative permeability (kr) can be measured in the laboratory using steady-state and
unsteady-state methods, or estimated by mathematical correlations and pore-network models. As multi-phase flow experiments and in particular steady-state measurements are very time consuming and expensive, more often the unsteady-state method is used for multi-phase kr measurements. In this thesis, a methodology has been devised for
calculating kr values and in particular three-phase kr from unsteady-state experiments.
The effort was extended to simultaneously calculating Pc from the same coreflood
experiment.
There are different physical parameters which can affect flow functions. The effect of gas/oil interfacial tension (IFTg/o) on two and three-phase kr and also on residual
saturation during alternative water and gas injections has also been studied.
Finally, two-phase kr have been estimated for rock and fluid conditions where there is
no previous data. This has been achieved by taking data from different conditions under which measurements were made.
To my beloved wife and parents,
This work would never be possible without the support and collaboration I found within the Centre for Enhanced Oil Recovery and CO2 Solutions. First of all, I would like to
express my profound gratitude to Prof. Mehran Sohrabi for providing me the opportunity, financial support and encouragement throughout my study. Your office was always open when I had any question or concern. I am also thankful to Dr. Hamidreza Shahverdi who was my second supervisor during the first year of my study before he left to Isfahan University of Technology. I am most grateful for your invaluable guidance and all the constructive discussions and also for supporting me and my family when we arrived in Edinburgh. Many thanks go to Prof. Dabir Tehrani for his practical comments, positive criticism and encouragement. I was very lucky to get to know Dr. Ahmed Elsheikh. Thank you for sharing your knowledge and expertise in application of ensemble-based optimization algorithms and also for helping me to build a collaborative research work. A big thanks to Dr. Gillian Pickup and Prof. Fabio Inzoli for accepting to be my examiners and for your invaluable comments.
During my PhD I was fortunate enough to work with other academic staff. Prof. Mahmoud Jamiolahmady, thank you for believing in my well testing expertise and providing me the opportunity to work as a tutor and marker for your Well Testing course. Prof. Eric Mackay and Dr. Karl Stephen, I have learned a lot from the ECLIPSE tutorials for Reservoir Simulation course. Dr. Asghar Shams, I have gained a great deal of knowledge from tutorials for Formation Evaluation course. Thank you all for letting me to be part of the support team for these tutorials.
Thanks to the IPE computer support for providing me with all softwares needed to do my research study. Special thanks to Debbie Ross for all her administrative supports. Thanks to the International Student Advisors Office for their help with visa applications and the career advisers for helpful tips.
Special thanks go to my friends and colleagues at the Centre for Enhanced Oil Recovery and CO2 Solutions; Hassan Alzayer, Omid Shahrokhi, Usman Taura, Shokoufeh
Aghabozorgi, Juliana Facanha, Pedram Mahzari, S. Amir Farzaneh, Mehdi Seyyedsar, Mojtaba Seyyedi, Bruno Pereira, Bashir Alkhazmi, Latifa Al-Nuaimi, Mohamed AlHammadi, Ali Almesmari, Odilla Vilhena, Adel Traki, Shaun Ireland, Kamran Ahmed, and Pantelis Tsolis. Thanks are also extended to my friends at Heriot-Watt
Haghi, Morteza AminNaji, Morteza Haghighat Sefat, Saleh Godarzian, Mojtaba Moradi, Caroline Johnson, Houra Mozaffar, Hamidreza Nasriani, Khosro Jarrahian, Pezhman Ahmadi, Mahmoud Nazeri, Michael Wise, Payam Alikhani, Aliakbar Hassanpour, Masoud Ghaderi, Dennis Obidegwu, Christian Onwunyili, Misfer Almarri, and Ibrahim Abdulwahab. Special appreciation also goes to those who left the University, Jalal Foroozesh, Jalal Fahimpour, S. Mobeen Fatemi, Yousef Rafiei, Hamid Bazargan, S. Mohamad Shariatipour, Heron Gachuz, Reza Felahat, Reza Malakooti, Babak Zarei, Saeed Mazloom, Mohamed Ahmed, Gamal Alusta and Mustafa Lamorde.
My beloved wife, your support was infinite! I simply can’t thank you enough for your endless support, patience, love, and encouragement. Special thanks to my son, Ali, for his understanding, constant love and support. I am heavily indebted to my parents for their love, care and support. Without them, I would have achieved nothing. My hope, is to make you happy and be pleased with me.
v
Name: AMIR JAHANBAKHSH
School/PGI: EGIS/Institute of Petroleum Engineering
Version: (i.e. First, Resubmission, Final)
Final Degree Sought (Award and Subject area)
Ph.D. in Petroleum Engineering
Declaration
In accordance with the appropriate regulations I hereby submit my thesis and I declare that: 1) the thesis embodies the results of my own work and has been composed by myself 2) where appropriate, I have made acknowledgement of the work of others and have made
reference to work carried out in collaboration with other persons
3) the thesis is the correct version of the thesis for submission and is the same version as any electronic versions submitted*.
4) my thesis for the award referred to, deposited in the Heriot-Watt University Library, should be made available for loan or photocopying and be available via the Institutional
Repository, subject to such conditions as the Librarian may require
5) I understand that as a student of the University I am required to abide by the Regulations of the University and to conform to its discipline.
* Please note that it is the responsibility of the candidate to ensure that the correct version of the thesis is submitted.
Signature of Candidate: Date: Submission Submitted By (name in capitals): Signature of Individual Submitting: Date Submitted:
For Completion in the Student Service Centre (SSC)
Received in the SSC by (name in capitals):
Method of Submission
(Handed in to SSC; posted through internal/external mail):
E-thesis Submitted
(mandatory for final theses)
Signature: Date:
CHAPTER 1 – Introduction ... 1
1.1. Structure of the Thesis ... 5
1.2. References ... 7
CHAPTER 2 -Coreflood Experiments ... 10
2.1 Coreflood Facilities ... 11
2.1.1 Porous Media (Cores) and Fluids ... 11
2.1.2 Establishing Irreducible Water Saturation ... 14
2.1.3 Development of Mixed-Wettability ... 15
2.1.4 Capillary Pressure Data ... 16
2.2 Coreflood Experiments ... 17
2.3 References ... 18
CHAPTER 3 – Estimation of Three-Phase Relative Permeability (kr) from Unsteady-State Coreflood Experiments ... 19
3.1 Introduction ... 20
3.2 Automatic History Matching ... 23
3.2.1 Mathematical Model (Coreflood Simulation) ... 24
3.2.2 Functional Form of Relative Permeability (kr) ... 26
3.2.3 Optimization Algorithm (Genetic Algorithm) ... 31
3.2.4 Application for Two-Phase Coreflood Experiments ... 33
3.3 Experiments, Results, and Discussion ... 34
3.3.1 Experiments... 34
3.3.2 History Matching Results ... 37
3.4 Conclusions ... 44
3.5 References ... 44
CHAPTER 4 - Simultaneous Estimation of Relative Permeability and Capillary Pressure from Coreflood Experiments ... 47
4.1 Introduction ... 48
4.2 New Methodology ... 50
4.2.1 Theoretical Background ... 50
4.2.2 Estimation Procedure ... 53
4.3 Verification of Methodology, Results, and Discussion ... 55
4.3.1 Experimental Data ... 55
Independent kr & Pc Functions ... 60
4.3.4 Discussion ... 63
4.4 Conclusions ... 65
4.5 References ... 66
CHAPTER 5 – Effect of Gas/Oil IFT on Two- and Three-Phase Relative Permeability and Residual Oil Saturation ... 68
5.1 Introduction ... 69
5.1.1 Effect of IFT on Two-Phase Relative Permeability ... 69
5.1.2 Effect of IFT on Three-Phase Relative Permeability ... 72
5.1.3 IFT Scaling Methods ... 73
5.2 Experiments and History Matching ... 75
5.2.1 Two-Phase Flow Experiments ... 75
5.2.2 Three-Phase Flow Experiments ... 77
5.3 Results and Discussion ... 78
5.3.1 Two-Phase Relative Permeability ... 78
5.3.2 Three-Phase Relative Permeability ... 80
5.3.3 Two-Phase IFT Scaling Methods ... 81
5.4 Effect of Gas/Oil IFT on the Residual Oil Saturation in Water-Alternating-Gas (WAG) Injections at Laboratory Scale ... 86
5.4.1 Summary of the results at HWU ... 87
5.4.2 Published Literature ... 89
5.5 Conclusions ... 96
5.6 References ... 98
CHAPTER 6 – Gas/Oil Relative Permeability Normalization ... 101
6.1 Introduction ... 102
6.2 Theory & Methodology ... 103
6.3 Experiments ... 105
6.4 Results & Discussion ... 106
6.4.1 Effect of absolute permeability ... 107
6.4.2 Effect of wettability... 108
6.4.3 Effect of gas/oil IFT ... 110
6.4.4 Application of Dynamic Trap Saturation ... 111
6.5 Conclusions ... 112
6.6 References ... 113
Chapter 4 ... 116
Chapter 5 ... 117
Chapter 6 ... 117
Recommendations and Future Works ... 118
APPENDICES ... 120
Appendix A: Measured and Estimated kr in Chapter 6 ... 120
FIGURE 2-1:HIGH-PRESSURE COREFLOOD FACILITY USED FOR DISPLACEMENT TESTS. ... 11 FIGURE 2-2: POROSITY PROFILE ALONG THE 65 MDCLASHACH SANDSTONE CORE SAMPLE. ... 12 FIGURE 2-3: PORE SIZE DISTRIBUTION OF CLASHACH SANDSTONE IN A WIDE RANGE OF
PERMEABILITY. ... 13 FIGURE 2-4: ESTABLISHED IMMOBILE WATER SATURATION ALONG THE CORE, OBTAINED FROM
X-RAY FOR 65MD WATER-WET AND MIXED-WET CORES. ... 15 FIGURE 2-5:(A)ESEM PICTURE FOR A THIN SECTION OF WATER-WET ROCK:WATER FILMS
WERE FORMED ON THE GRAINS (B)ESEM PICTURE FOR A THIN SECTION OF MIXED-WET ROCK:WATER FORMED DROPLETS ON THE GRAIN SURFACES RATHER THAN FILMS. ... 16 FIGURE 2-6:MEASURED AIR-MERCURY CAPILLARY PRESSURE FOR 1000 MD WATER-WET CORE.
... 17 FIGURE 2-7:MEASURED OIL/WATER CAPILLARY PRESSURE OBTAINED DURING USBM
WETTABILITY DETERMINATION TEST CARRIED OUT ON 1093 MD MIXED-WET CORE
(SOHRABI ET AL.2007). ... 17 FIGURE 3-1:THREE-PHASE UNSTEADY-STATE COREFLOOD EXPERIMENT.ONE FLUID DISPLACES
THE RESIDENT PHASES. ... 21 FIGURE 3-2:WORKFLOW FOR DETERMINATION OF THREE PHASE KR VALUES FROM UNSTEADY
-STATE COREFLOOD EXPERIMENT ... 24 FIGURE 3-3:HORIZONTAL CORE AND EQUIVALENT 1DCARTESIAN GRIDDING IN X DIRECTION.
... 26 FIGURE 3-4:CHROMOSOME1 WHICH IS A SET OF ALL THREE-PHASE RELATIVE PERMEABILITIES
(KRO, KRW, AND KRG). ... 32
FIGURE 3-5:GENES IN THE WATER RELATIVE PERMEABILITY. ... 32 FIGURE 3-6:GENETIC ALGORITHM FOR OBTAINING KR FROM A COREFLOOD EXPERIMENT. ... 33
FIGURE 3-7:COMPARISON OF THREE-PHASE SATURATION PATHS FOR FIRST GAS INJECTIONS IN
65 MD WATER-WET (GREEN) AND MIXED-WET (RED) CORES. ... 35 FIGURE 3-8:CUMULATIVE OIL PRODUCTION FOR FIRST GAS INJECTION IN 65 MD WATER-WET
CORE. ... 35 FIGURE 3-9:PRESSURE DROP ACROSS THE CORE FOR FIRST GAS INJECTION IN 65 MD WATER
-WET CORE. ... 36 FIGURE 3-10:CUMULATIVE OIL PRODUCTION FOR FIRST GAS INJECTION IN 65 MD MIXED-WET
CORE. ... 36 FIGURE 3-11:PRESSURE DROP ACROSS THE CORE FOR FIRST GAS INJECTION IN 65 MD MIXED
-WET CORE ... 37 FIGURE 3-12:THE MINIMUM MISFIT AND AVERAGE MISFIT PER 100 ITERATIONS FOR HISTORY
MATCHING OF 1ST
PRODUCTION FOR 1ST
GAS INJECTION IN 65 MD MIXED-WET CORE.SWI THREE-PHASE KRO
FUNCTION WAS USED. ... 38 FIGURE 3-14:COMPARISON BETWEEN HISTORY MATCHING AND EXPERIMENT PRESSURE DROP
FOR 1ST
GAS INJECTION IN 65 MD MIXED-WET CORE.SWI THREE-PHASE KRO FUNCTION WAS
USED. ... 39 FIGURE 3-15:COMPARISON BETWEEN HISTORY MATCHING AND EXPERIMENT CUMULATIVE OIL
PRODUCTION FOR 1ST GAS INJECTION IN 65 MD MIXED-WET CORE.ST1 THREE-PHASE KRO
FUNCTION WAS USED. ... 39 FIGURE 3-16:COMPARISON BETWEEN HISTORY MATCHING AND EXPERIMENT PRESSURE DROP
FOR 1ST
GAS INJECTION IN 65 MD MIXED-WET CORE.ST1 THREE-PHASE KRO FUNCTION WAS
USED. ... 40
FIGURE 3-17:COMPARISON BETWEEN HISTORY MATCHING AND EXPERIMENT CUMULATIVE OIL
PRODUCTION FOR 1ST
GAS INJECTION IN 65 MD WATER-WET CORE.SWI THREE-PHASE KRO
FUNCTION WAS USED. ... 40 FIGURE 3-18:COMPARISON BETWEEN HISTORY MATCHING AND EXPERIMENT PRESSURE DROP
FOR 1ST
GAS INJECTION IN 65 MD WATER-WET CORE.SWI THREE-PHASE KRO FUNCTION WAS
USED. ... 41 FIGURE 3-19:ESTIMATED THREE-PHASE OIL (TOP), GAS (MIDDLE) AND WATER (BOTTOM)
RELATIVE PERMEABILITIES FROM UNSTEADY-STATE GAS INJECTION IN 65 MD MIXED-WET CORE. ... 42 FIGURE 3-20:ESTIMATED THREE-PHASE OIL (TOP), GAS (MIDDLE) AND WATER (BOTTOM)
RELATIVE PERMEABILITIES FROM UNSTEADY-STATE GAS INJECTION IN 65 MD WATER-WET CORE. ... 43 FIGURE 4-1:GENETIC ALGORITHM FOR SIMULTANEOUS COMPUTATION OF KR AND PC FROM A
COREFLOOD EXPERIMENT ... 55 FIGURE 4-2:CUMULATIVE WATER PRODUCTION (CM3) FOR UNSTEADY-STATE COREFLOOD
EXPERIMENT (SUN &MOHANTY (2005)). ... 56 FIGURE 4-3:PRESSURE DROP (PSI) ACROSS FOR UNSTEADY-STATE COREFLOOD EXPERIMENT
(SUN &MOHANTY (2005)). ... 56 FIGURE 4-4:IN-SITU SATURATION PROFILES AT DIFFERENT TIMES DURING THE UNSTEADY
-STATE COREFLOOD EXPERIMENT (SUN &MOHANTY (2005)). ... 57 FIGURE 4-5:ESTIMATED OIL/WATER RELATIVE PERMEABILITY FROM THE UNSTEADY-STATE
COREFLOOD EXPERIMENT (ZHANG ET AL.(2012)). ... 58 FIGURE 4-6:ESTIMATED PCOW FROM THE UNSTEADY-STATE COREFLOOD EXPERIMENT (ZHANG
ET AL.(2012)). ... 58 FIGURE 4-7:COMPARISON OF CUMULATIVE WATER PRODUCTION VERSUS INJECTION TIME FOR
SIMULATION AND EXPERIMENTAL DATA, WHEN KR AND PC ARE RELATED. ... 59
FIGURE 4-8:COMPARISON OF PRESSURE DROP VERSUS INJECTION TIME FOR SIMULATION AND EXPERIMENTAL DATA, WHEN KR AND PC ARE RELATED. ... 59
FIGURE 4-9:COMPUTED OIL AND WATER KR FROM COREFLOOD EXPERIMENT, WHEN KR AND PC
AND PC ARE RELATED. ... 60
FIGURE 4-11:COMPARISON OF CUMULATIVE WATER PRODUCTION VERSUS INJECTION TIME FOR SIMULATION AND EXPERIMENTAL DATA, WHEN KR AND PC ARE TWO INDEPENDENT
FUNCTIONS. ... 61 FIGURE 4-12:COMPARISON OF PRESSURE DROP VERSUS INJECTION TIME FOR SIMULATION AND
EXPERIMENTAL DATA, WHEN KR AND PC ARE TWO INDEPENDENT FUNCTIONS. ... 62
FIGURE 4-13:ESTIMATED OIL/WATER KR FROM COREFLOOD EXPERIMENT WHEN KR AND PC ARE
TWO INDEPENDENT FUNCTIONS. ... 62 FIGURE 4-14:ESTIMATED CAPILLARY PRESSURE (PSI) FROM COREFLOOD EXPERIMENT WHEN KR
AND PC ARE TWO INDEPENDENT FUNCTIONS. ... 63
FIGURE 4-15:COMPARISON OF COMPUTED NORMALIZED KR BY ZHANG ET AL.(2012)(MARKER
POINTS) AND THOSE USING TWO METHODS OF: ... 64 FIGURE 4-16:COMPARISON OF COMPUTED PC(PSI) BY ZHANGET AL.(2012)(MARKER POINTS)
AND THOSE USING THE TWO METHODS OF: ... 65 FIGURE 5-1:OIL AND GAS RELATIVE PERMEABILITIES FOR IFT VALUES GREATER THAN 0.04
MNM-1(AFTER BARDON AND LONGERON (1980)). ... 70 FIGURE 5-2:OIL AND WATER RELATIVE PERMEABILITIES FOR DIFFERENT IFT VALUES (AFTER
SHEN ET AL.(2006))... 72 FIGURE 5-3:EXPERIMENTAL AND HISTORY MATCHED PRODUCTION DATA AND PRESSURE DROP
FOR THE GAS INJECTION PERFORMED IN 65 MD MIXED-WET CORE AT GAS/OIL IFT=0.15
MN.M-1. ... 76 FIGURE 5-4:EXPERIMENTAL AND HISTORY MATCHED PRODUCTION DATA AND PRESSURE DROP
FOR THE GAS INJECTION PERFORMED IN 65 MD MIXED-WET CORE AT GAS/OIL IFT=2.70
MN.M-1. ... 76 FIGURE 5-5:EXPERIMENTAL AND HISTORY MATCHED OIL PRODUCTION AND PRESSURE DROP
DATA FOR THE 1ST
GAS INJECTION PERIOD OF THE WAG PERFORMED IN 65 MD MIXED-WET CORE AT IFTG/O=0.15 MN.M-1. ... 77
FIGURE 5-6:EXPERIMENTAL AND HISTORY MATCHED OIL PRODUCTION AND PRESSURE DROP DATA FOR THE 1ST
GAS INJECTION PERIOD OF THE WAG INJECTION PERFORMED IN 65 MD
MIXED-WET CORE AT IFTG/O=2.70 MN.M-1. ... 77
FIGURE 5-7:GAS AND OIL RELATIVE PERMEABILITIES FOR THE GAS INJECTIONS PERFORMED IN
1000 MD WATER-WET CORE AT DIFFERENT GAS/OIL IFT(IFT=2.70 AND 0.04 MN.M-1). .. 79 FIGURE 5-8:GAS AND OIL RELATIVE PERMEABILITIES FOR THE GAS INJECTIONS PERFORMED IN
1000 MD MIXED-WET CORE AT DIFFERENT GAS/OIL IFT(IFT=2.70 AND 0.04 MN.M-1). ... 79 FIGURE 5-9:GAS AND OIL RELATIVE PERMEABILITIES FOR THE GAS INJECTIONS PERFORMED IN
65 MD MIXED-WET CORE AT DIFFERENT GAS/OIL IFT(IFT=2.70,0.15 AND 0.04 MN.M-1).79 FIGURE 5-10:OIL RELATIVE PERMEABILITIES FOR THE GAS INJECTIONS PERFORMED IN 65 MD
MIXED-WET CORE AT DIFFERENT GAS/OIL IFT(IFT=2.70,0.15 AND 0.04 MN.M-1). ... 81 FIGURE 5-11:GAS RELATIVE PERMEABILITIES FOR THE GAS INJECTIONS PERFORMED IN 65 MD
MD MIXED-WET CORE AT DIFFERENT GAS/OIL IFT(IFT=2.70,0.15 AND 0.04 MN.M-1). ... 81 FIGURE 5-13:MEASURED GAS AND OIL RELATIVE PERMEABILITIES 1000 MD MIXED-WET CORE
AT IFT OF 2.7 MNM-1. ... 82 FIGURE 5-14:COMPARISON OF OIL RECOVERY (%IOIP) BETWEEN SIMULATION WHILE IGNORING
THE EFFECT OF IFT AND SIMILAR EXPERIMENT PERFORMED AT LOW GAS/OIL IFT OF 0.04
MNM-1. ... 83 FIGURE 5-15:COMPARISON OF PRESSURE DROP (PSI) BETWEEN SIMULATION, WHILE IGNORING
THE EFFECT OF IFT AND SIMILAR EXPERIMENT PERFORMED AT LOW GAS/OIL IFT OF 0.04
MNM-1. ... 83
FIGURE 5-16:COMPARISON OF OIL RECOVERY (%IOIP) BETWEEN RESULTS OF A SIMULATION USING COATS METHOD AND EXPERIMENT AT LOW GAS/OIL IFT OF 0.04 MNM-1. ... 84
FIGURE 5-17:COMPARISON OF PRESSURE DROP (PSI) BETWEEN RESULTS OF A SIMULATION USING COATS METHOD AND EXPERIMENT AT LOW GAS/OIL IFT OF 0.04 MNM-1. ... 84
FIGURE 5-18:COMPARISON OF OIL RECOVERY (%IOIP) BETWEEN RESULTS OF SIMULATION USING MODIFIED COATS METHOD AND EXPERIMENT AT LOW GAS/OIL IFT CONDITIONS.... 86
FIGURE 5-19:COMPARISON OF PRESSURE DROP (PSI) BETWEEN RESULTS OF SIMULATION USING MODIFIED COATS METHOD AND EXPERIMENT AT LOW GAS/OIL IFT CONDITIONS ... 86 FIGURE 5-20:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING
WAG-ID INJECTIONS IN 65 AND 1000 MD MIXED-WET CORES. ... 89 FIGURE 5-21:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING
WAG-DI INJECTIONS IN 65 MD MIXED-WET CORE. ... 89 FIGURE 5-22:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING
WAG-DI(BLUE) AND WAG-ID(RED) FOR BEREA SANDSTONE AND R1NORTH SEA
CORES. ... 91 FIGURE 5-23:RESIDUAL OIL SATURATION AFTER IMMISCIBLE WAG WITH SWELLING (RED) AND
WITHOUT SWELLING (BLUE) FOR A WATER-WET SANDSTONE CORE. ... 92 FIGURE 5-24:COMPARISON OF RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING
PHASE DURING WAG-ID EXPERIMENTS, PERFORMED BY MINSSIEUX (RED) AND HWU (BLUE)... 93 FIGURE 5-25:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING WAG
TESTS THAT STARTED WITH DIFFERENT INITIAL OIL AND WATER SATURATIONS. ... 94 FIGURE 5-26:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING
WAG-DI(BLUE) AND WAG-ID(RED)WAG INJECTIONS BY ELEMENT ET AL. AND SKAUGE
&LARSEN. ... 95 FIGURE 5-27:RESIDUAL OIL SATURATION AT THE END OF EACH FLOODING PHASE DURING
WAG-ID INJECTIONS BY ELEMENT ET AL.(RED) AND HWU(BLUE). ... 96 FIGURE 6-1: OPTIMAL PARAMETERS Α AND Β AS FUNCTIONS OF THE INTRINSIC CONTACT ANGLE
(AFTER SPITERI ET AL.2005). ... 105 FIGURE 6-2:(A)COMPARISON OF MEASURED GAS/OIL RELATIVE PERMEABILITIES FOR
PERMEABILITIES OF 1000 MD WATER-WET CORE WERE USED IN ESTIMATION. ... 107 FIGURE 6-3:(A)COMPARISON OF MEASURED GAS/OIL RELATIVE PERMEABILITIES FOR
EXPERIMENTS 2 AND 4.(B)COMPARISON BETWEEN MEASURED AND ESTIMATED GAS/OIL RELATIVE PERMEABILITIES FOR 65 MD MIXED-WET CORE.MEASURED GAS/OIL RELATIVE PERMEABILITIES OF 1000 MD MIXED-WET CORE WERE USED IN ESTIMATION. ... 108 FIGURE 6-4:(A)COMPARISON OF MEASURED GAS/OIL RELATIVE PERMEABILITIES FOR
EXPERIMENTS 1 AND 2.(B)COMPARISON BETWEEN MEASURED AND ESTIMATED GAS/OIL RELATIVE PERMEABILITIES FOR 65 MD MIXED-WET CORE.MEASURED GAS/OIL RELATIVE PERMEABILITIES OF 65 MD WATER-WET CORE WERE USED IN ESTIMATION.MW=MIXED -WET;WW=WATER-WET. ... 109 FIGURE 6-5:COMPARISON OF MEASURED GAS/OIL RELATIVE PERMEABILITIES FOR
EXPERIMENTS 3 AND 4.MW= MIXED-WET;WW= WATER-WET. ... 109 FIGURE 6-6:(A)COMPARISON OF GAS/OIL RELATIVE PERMEABILITIES FOR EXP#5 AND 6.(B)
COMPARISON BETWEEN MEASURED AND ESTIMATED GAS/OIL RELATIVE PERMEABILITIES FOR 1000 MD MIXED-WET CORE.MEASURED GAS/OIL RELATIVE PERMEABILITIES OF 1000 MD WATER-WET CORE WERE USED IN ESTIMATION. ... 110 FIGURE 6-7:(A)COMPARISON OF GAS/OIL RELATIVE PERMEABILITIES FOR EXPERIMENTS 3 AND
5.(B)COMPARISON BETWEEN MEASURED AND ESTIMATED GAS/OIL RELATIVE PERMEABILITIES FOR 1000 MD WATER-WET CORE AT LOW IFT.MEASURED GAS/OIL RELATIVE PERMEABILITIES OF 1000 MD WATER-WET CORE AT HIGH IFT WERE USED IN ESTIMATION. ... 111 FIGURE 6-8:(A)DYNAMIC TRAPPED OIL SATURATION VERSUS OIL SATURATION FOR
EXPERIMENTS 1 AND 2.(B)COMPARISON BETWEEN MEASURED AND ESTIMATED GAS/OIL RELATIVE PERMEABILITIES FOR 65 MD MIXED-WET CORE.MEASURED GAS/OIL RELATIVE PERMEABILITIES OF 65 MD WATER-WET CORE AND DYNAMIC TRAP SATURATIONS WERE USED IN ESTIMATION. ... 112
The research material in this thesis was part of the research program of a joint industry project (JIP) referred to as “Improved Characterization of Two- and Three-Phase Flow for Reliable Reservoir Performance Prediction”. The results of this research have been reported, presented and discussed every six months in the corresponding steering committee meetings during Sep.2012-April.2016.
Furthermore, parts of the results of this study have been submitted as technical papers in different international conferences and peer-reviewed journals.
A list of these publications is as follows:
Jahanbakhsh, A., Shahverdi, H. & Sohrabi, M. (2016): “Gas/Oil Relative Permeability Normalization- Effect of Permeability, Wettability and Interfacial tension”, SPE Reservoir Evaluation & Engineering-Formation Evaluation, SPE-170796-PA. http://dx.doi.org/10.2118/170796-PA.
Jahanbakhsh, A., Sohrabi, M., Fatemi, S. M. and Shahverdi, H. (2016): “A Comparative Study of the Effect of Gas/Oil IFT Variation on Two- and Three-Phase Relative Permeability and the Performance of WAG Injection at
Laboratory Scale”, SPE-179571-MS, SPE Improved Oil Recovery Conference, Tulsa, Oklahoma 2016. http://dx.doi.org/10.2118/179571-MS.
Jahanbakhsh, A., and Sohrabi, M. (2015): “A New Approach for Simultaneous
Estimation of Relative Permeability and Capillary Pressure from Coreflood Experiments”, SPE-175068-MS, Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas 2015.
http://dx.doi.org/10.2118/175068-MS.
Jahanbakhsh, A., Shahverdi, H. and Sohrabi, M. (2014): “Relative
Permeability Normalization- Effect of Permeability, Wettability and Interfacial tension”, SPE-170796-MS, Paper presented at the SPE Annual Technical
Conference and Exhibition, Amsterdam 2014. http://dx.doi.org/10.2118/170796-MS.
Jahanbakhsh, A., El Sheikh, A. and Sohrabi, M., (2016): “Application of
Ensemble Smoother and Multiple-Data Assimilation for Estimating Relative Permeability from Coreflood Experiments”, accepted for the 15th European Conference on the Mathematics of Oil Recovery (ECMOR XV), Amsterdam 2016.
Chapter 1– Introduction
Multi-phase flow and in particular three-phase flow in porous media is one of the very active research areas in both petroleum and environmental engineering. In the oil industry, two- and three-phase flow occurs in secondary recovery and Enhanced Oil Recovery (EOR) processes including waterflooding, gas injection, tertiary gas injection, water alternating gas injection, depressurization below the bubble point, gas cap expansion, solution gas drive, gravity drainage, steam injection and thermal flooding. In the environmental engineering context, multi-phase flow occurs when a non-aqueous phase liquid (NAPL) flows simultaneously with water and air through soils and also CO2 storage in aquifers and geological formations.
In the petroleum engineering context, recovery of a significant amount of the residual oil in reservoirs after primary recovery and secondary recovery is important in order to tackle the growing world’s demand for the energy. Therefore, there is a need to seek means of recovering more of the residual oil left in the reservoirs. Hence, several EOR techniques have been developed to recover economically a significant portion of this residual oil which maybe around 40 to 60% of the original oil in place. The majority of these methods mainly involve two and three-phase flow at different parts of the reservoir. Some of these methods have sequential drainage and imbibition processes such as Water-Alternating-Gas (WAG) injection which add the effect of hysteresis to the complexity of the fluid flow behaviour. Relative permeability (kr) and capillary
pressure (Pc) are two critical parameters in multiphase flow which describe the
interaction of each fluid in porous media. The importance of these flow functions will be even more significant for three-phase flow systems. These are the input parameters to the reservoir simulation for modelling the fluid flow in porous media, history matching the recovery mechanisms and predicting the future performance of the reservoirs.
Extensive laboratory measurements and modelling efforts have been performed in two-phase flow area for several decades, but that is not the case for three-two-phase relative permeability (kr). The fewer efforts in three-phase flow are mainly because three-phase
flow experiments, and in particular steady-state measurements, are very complicated, labour intensive, time-consuming and expensive. Furthermore, the presence of three fluid phases at the same time, means two independent fluid saturations, produces an infinite number of saturation paths as possible candidates for fluid flow study and kr
measurements. Therefore, it is not practical to measure kr for all possible three-phase
saturation paths.
Traditionally, two-phase relative permeabilities are measured in a Special Core Analysis (SCAL) program for some available core samples. Although this practice has been established in the oil and gas industry, it is still impractical to measure two-phase relative permeabilities for hundreds of core samples to cover difference regions of a reservoir or a field. Plausible and robust methods are required to estimate relative permeabilities for the regions where no core sample or measurement is available. The effect of different parameters such as absolute permeability, wettability, interfacial tension (IFT) on kr should be properly included in such a predictive method. The kr and Pc curves are conventionally measured separately and sometimes even from two different core samples. Capillary pressure is measured by: mercury porosimetry, the porous plate method or by the centrifuge method. Using these methods, Pc is measured
at equilibrium conditions and it can be called static Pc. The equilibrium conditions may
not be achievable during multi-phase flow in porous media. The fluid flow is a dynamic process, and there has been a question around the application of static Pc for modeling
of this process. Moreover, it is not known whether there are any differences between static and dynamic Pc. Therefore, the simultaneous estimation of kr and Pc from
coreflood experiments to obtain dynamic Pc has gained more interest.
In the last three decades, more attentions has been paid to three-phase flow mechanisms and specially three-phase relative permeability. Leverett and Lewis (1941) measured the first three-phase relative permeabilities using the steady-state method. Alizadeh and Piri (2014) reviewed experimental studies on three-phase kr since 1980.These studies were
involved with investigating the effect of wettability, IFT, spreading, oil layer drainage and saturation history on three-phase flow functions. Some of these studies are highlighted in the following paragraphs.
A example of a research study on the effect of wettability at three-phase flow conditions is the extensive work by Oak (1990). He measured steady-state three-phase kr for
different wettability conditions of water-wet, oil-wet and intermediate-wet on Berea sandstone cores. DiCarlo et al. (1998) studied three-phase flow in sand packs for three wettability conditions of water-wet, oil-wet, and fractionally-wet. They used a CT scanning method to measure the oil and water relative permeabilities.
A limited number of studies have investigated the impact of IFT on three-phase relative permeabilities. Delshad et al. (1987) measured steady-state two- and three-phase kr for
low IFT mixture of brine/oil/surfactant/alcohol in Berea sandstone cores. Dria et al. (1993) reported steady-state three phase CO2/oil/brine relative permeabilities in a
water-wet dolomite core. Cinar and Orr (2004) and Cinar and Orr (2005) investigated the effect of IFT reduction on three-phase relative permeabilities for water-wet wettability condition using three-phase analogous liquid systems. Cinar et al. (2004) and (2007) reported three-phase kr measurements that included the combined effects of IFT
variation and wettability.
A research study on characterization of three-phase flow in porous media was initiated in 1997 at Heriot-Watt University. The experimental research work was started using micro-models. An extensive list of micromodel experiments in two-phase and mainly three-phase flow in the form of WAG injections were performed at different wettability conditions (water-wet, mixed-wet and oil-wet). The results of these micromodel experiments showed that the residual oil saturation to secondary water flooding or secondary gas injection decreases at three-phase flow conditions. Therefore, the experimental study was extended to the core scale displacement experiments (Sohrabi et al. (2000, 2005 and 2008)). The coreflood studies started with series of two-phase displacement experiments in water-wet and mixed-wet 1000 mD Clashach sandstone core at high (2.7 mNm-1) and very low (0.04 mNm-1) IFT conditions (Sohrabi et al. (2007)). A series of three-phase flow and WAG injections was performed on 1000 mD mixed-wet core at the IFT above values. The next set of coreflood experiments was conducted on 65 mD Clashach sandstone core. Similar to the 1000 mD corefloods, two different wettability of water-wet and mixed-wet and different gas/oil IFT conditions were considered in these series of experiments. In summary, the effect of rock permeability, wettability, and gas/oil IFT conditions were studied for two- and three-phase flow systems (Fatemi et al. (2011, 2012 and 2015)).
As it was mentioned before, it is not practical to measure kr for all possible three-phase
saturation paths. Furthermore, for the purpose of numerical simulation, it is preferred to have a correlation to estimate the three-phase relative permeabilities accurately. Stone (1970) introduced a probability method which uses two-phase kr data for oil/water and
gas/oil systems to predict the three-phase oil relative permeability. In 1973, Stone modified his first models by including two-phase gas and water kr into the formulation.
permeabilities are only function of their saturations. Modification to the Stone’s first model was suggested by Hustad and Holt (1992). They introduced an exponent to the saturation term of the correlation and used that exponent as a tuning parameter to obtain a better match between results of their numerical simulation and experiment.
Baker (1988) proposed an interpolation method to calculate three-phase kr for all three
phases (oil, water, and gas) using two-phase kr data. In his method, three-phase kr of
each phase is assumed to be a function of saturations of two other phases. Hustad and Hansen (1995), proposed a model for three-phase relative permeabilities which had the basis of Baker’s model. Later, Hustad and Browning (2010) proposed a formulation to calculate three-phase kr and Pc and account for hysteresis for compositional simulation.
Blunt (2000) introduced a model based on saturation-weighted interpolation between the two-phase relative permeabilities. The special feature of this model is accounting for oil layer drainage in the calculation of relative permeability. Other different models have been developed to predict three-phase kr from two-phase kr data, such as Jerauld (1997) and UTKR3P (2013).
Delshad et al. (1987); Delshad and Pope (1989), Pejic and Maini (2003), Petersen et al. (2008) and some other researchers have undertaken studies to evaluate the performance of the existing three-phase kr models in predicting kr values. The common conclusion
from these assessment studies is that none of the models can predict the measured three-phase relative permeabilities from different sources. These studies showed that the three-phase kr models are not capable of accounting for the effect of different
wettability, interfacial tension, and saturation directions. Therefore, an extensive bank of three-phase experimental data and kr is required to characterize three-phase flow in
porous media and propose a robust predictive three-phase kr model.
It is worth mentioning that the concept of Pc is still an ambiguous subject in three-phase
flow systems, and more research should be performed to shed light on this area.
The general theme of the thesis is a characterization of multiphase flow in porous media. The overall purpose is to address some issues in two- and three-phase flow systems which are still outstanding. This research was carried out alongside extensive experimental research studies. The objective of the research is to (i) develop a methodology and a computer program to estimate flow functions (kr and Pc) from the
two- and three-phase coreflood experiments, (ii) Secondly, by having the developed program there is a facility to estimate kr for different phases in multiphase flow
conditions and to characterize this flow function, (iii) as it is not always possible to perform either steady-state or unsteady state coreflood experiments for the purpose of measuring relative permeability, a normalization technique was introduced, evaluated and improved in order to estimate a kr curve from already measured kr curves obtained
from another rock which might have different rock permeability, wettability and IFT conditions.
1.1. Structure of the Thesis
Chapter 1&2- The first chapter of the thesis highlights the motivations behind this
work and introduces different aspects of the performed research study. The second chapter presents the experimental procedures and the facilities used in the Centre for Enhanced Oil Recovery and CO2 Solutions at Heriot-Watt University for performing the
coreflood preparations and experiments. The hydrocarbon fluids and brine and also rock properties are summarized. Different preparation procedures including establishing initial water saturation and alternating wettability to mixed-wet wettability have been elaborated in detail.
Chapter 3- This chapter is devoted to highlighting the importance of measuring
three-phase kr curves. We explain the methodology of estimating this flow function from
measured unsteady-state coreflood experiments (two- and three-phase) results. Usually, the recovery of different phases and pressure drop across the core are measured during an experiment. The most common explicit method to calculate kr from the measured
results is the Johnson–Bossler–Naumann (JBN) method (Johnson et al. (1959)). In the implicit or parameter estimation method, kr values are estimated using history matching
technique. A functional form of kr containing tuning parameters is selected for each
phase, and an advanced optimization technique is used to match the experimental data to the simulation results. The process of history matching is an iterative process, and it is repeatedly attempted by changing the tuning parameters within the functional form of
kr until the closest match is obtained. The implicit method has been selected for estimating kr and by using MATLAB a computer program developed and Genetic
Algorithm implemented as the non-linear global optimizer. This program can estimate two- and three-phase kr curves from two- and three-phase unsteady state coreflood
experiments respectively.
Chapter 4- Chapter 4 is dedicated to simultaneous estimation of two critical flow
functions have been conventionally measured separately, and the measurements are not usually performed on the same rock sample. The drawback to determining kr and Pc
separately is that they may not be consistent with each other, and the measured Pc does
not correspond to the kr which is measured from a dynamic flow system. Therefore,
simultaneous determination of Pc and kr for a given system would be preferred. History
matching techniques have been applied to estimate kr and Pc simultaneously from
unsteady state coreflood experiments. Some in-situ measurements such as saturation and pressure profiles may be included in the history matching data to reduce the associated non-uniqueness problem of history matching, but this information is rarely available. Conventionally, two independent functions were used to generate these two flow functions in the process of the history matching. A new methodology has been developed to honour a known relationship between the core kr and the Pc curve and to
improve the optimization process and the accuracy of the estimated Pc and kr. Making
the kr function dependent on the Pc in the history matching process will reduce the
number of tuning parameters and is expected to reduce the uncertainty associated with the history matching process.
Chapter 5- The effect of gas/oil IFT on two- and three-phase relative permeabilities has
been studied in Chapter 5. Firstly we investigated the effects of gas/oil IFT reduction on two- and three-phase relative permeabilities according to the literature and the results of our experimental studies on 65 and 1000 mD cores at three different gas/oil IFT values of 0.04, 0.15 and 2.7 mN.m-1. We used the developed computer program to estimate two- and three-phase relative permeabilities from the results of coreflood experiments. The general perception is that the IFT reduction results in an increase in kr of existing
phases at each saturation value. A significant amount of studies have been performed on the two-phase systems and although there is no single conclusion but more insight has been gained on the effect of IFT reduction on the two-phase kr. However, for the
three-phase system, there is still a long journey to take in, to appreciably understand and model the effect of IFT change on the three-phase kr. The Second objective is to
evaluate the frequently used Coats IFT scaling method against our two-phase experimental data. The common practice is that the two-phase kr is usually measured at
high IFT values and for simulating a process that has to change IFT value, towards miscible conditions, a modification is applied to the high IFT kr data to calculate their
value at lower values of IFT. Application of this method has been evaluated for two-phase data.
Chapter 6-The objective of Chapter 6 is to predict the gas/oil kr for new rock/fluid
conditions (i.e., permeability, wettability, IFT) using existing gas/oil kr data measured at
different conditions. Using measured data from coreflood experiments, we showed that by applying an appropriate normalization technique, one can adequately predict kr of
rocks with different permeability and wettability conditions in two-phase gas/oil flow. However, the results showed that the effect of IFT change cannot be captured by normalization techniques. A new hypothesis has been introduced and proposed here based on Dynamic Trap Saturation to improve the methodology. Finally, the aim is to devise ways and means of estimating relative permeabilities, using available kr data of
one set of rocks and relevant fluid conditions, for different rocks and conditions. We have measured two-phase gas/oil kr for two Clashach sandstone cores with similar pore
size distribution and absolute permeability of 65 and 1000 mD, under mixed-wet and water-wet conditions, with low and high gas/oil IFT.
Chapter 7- Finally in Chapter 7 the conclusions drawn from this research study are
summarized. Moreover, recommendations for further and future works in the relevant research areas are presented.
1.2. References
Alizade, A. H. and Piri, M., 2014. Three-Phase Flow in Porous Media: A Review of Experimental Studies on Relative Permeability. Reviews of Geophysics, 2013RG000433.
Baker, L.E., 1988. Three-Phase Relative Permeability Correlations, paper SPE 17369, presented at the SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma.
Beygi, M. R., Delshad, M., Pudugramam, V. S., Pope, G. A. and Wheeler, M. F., 2013. A New Approach to Model Hysteresis and Its Impact on CO2-EOR Processes with Mobility Control Strategies. SPE Western Regional & AAPG Pacific Section Meeting, 2013 Joint Technical Conference. Monterey, CA, USA: Society of Petroleum Engineers.
Blunt, M.J., 2000. An Empirical Model for Three-Phase Relative Permeability: SPE Journal, paper SPE 67950, (12).
Cinar, Y. & Orr Jr., F. M., 2005. Measurement of Three-Phase Relative Permeability with IFT Variation. SPE Reservoir Evaluation & Engineering, 8, pp. 33-43.
Cinar, Y., Marquez, S., and Orr J., F. M., 2004. Effect of IFT Variation and Wettability on Three-Phase Relative Permeability. SPE Annual Technical Conference and Exhibition. Houston, Texas: Society of Petroleum Engineers.
Cinar, Y., Marquez, S., and Orr J., F. M., 2007, Effect of IFT Variation and Wettability on Three-Phase Relative Permeability: SPE Reservoir Evaluation & Engineering, paper SPE 90572-PA, (06).
Delshad, M., and Pope, G.A., 1989, Comparison of the three-phase oil relative permeability models: Transport in Porous Media, 4(1), p. 59-83.
Delshad, M., Delshad, M., Pope, G.A., and Lake, L.W., 1987, Two- and Three-Phase Relative Permeabilities of Micellar Fluids: SPE Formation Evaluation, paper SPE 13581, (09).
DiCarlo, D.A., Sahni, A., and Blunt, M.J., 1998, The Effect of Wettability on Three- Phase Relative Permeability, paper SPE 49317, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana.
Daria, D., Pope, G. A. and Sepehrnoori, K., 1993. Three-Phase Gas/Oil/Brine Relative Permeabilities Measured Under CO2 Flooding Conditions. SPE Reservoir Engineering, 8, 143-150.
Fatemi, S. M. and Sohrabi, M., 2015. Mechanistic Study of the Effect of Gas/Oil IFT on the Performance of Gas, WAG and SWAG Injections in Mixed-Wet Systems. SPE Annual Technical Conference and Exhibition held in Houston, Texas, USA, 28–30 September 2015.
Fatemi, S. M., Sohrabi, M., Ireland, S. and Jamiolahmady, M. 2012. Recovery Mechanisms and Relative Permeability for Oil/Gas System at Near-miscible Conditions: Effects of Immobile Water Saturation, Wettability, Hysteresis and Permeability. SPE Improved Oil Recovery Symposium. Tulsa, Oklahoma, USA, Society of Petroleum Engineers.
Fatemi, S. M., Sohrabi, M., Jamiolahmady, M., Ireland, S. and Robertson, G., 2011. Experimental Investigation of Near-Miscible Water-Alternating-Gas (WAG) Injection Performance in Water-wet and Mixed-wet Systems. Presented at Offshore Europe,Aberdeen,6–8September.SPE-145191-MS.
http://dx.doi.org/10.2118/145191-MS.
Hustad, O.S., and Browning, D.J., 2010. A Fully Coupled Three-Phase Model for Capillary Pressure and Relative Permeability for Implicit Compositional Reservoir Simulation: SPE Journal, paper SPE 125429-PA, (12).
Hustad, O.S., and Hansen, A.G., 1995. A Consistent Correlation for Three-Phase Relative Permeabilities and Phase Pressure Based on Three Sets of Two Phase Data, presented at the 8th European IOR Symposium, Vienna, Austria.
Hustad, O.S., and Holt, T., 1992. Gravity Stable Displacement of Oil by Hydrocarbon Gas after Waterflooding, paper SPE 24116, presented at the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma.
Jerauld, G., 1997. General Three-Phase Relative Permeability Model for Prudhoe Bay. SPE Res Eng 12 (4): 255–263. SPE-36178-PA. http://dx.doi.org/10.2118/36178-PA.
Johnson, E.F., Bossler, D.P., and Naumann, V.O., 1959. Calculation of Relative Permeability from Displacement Experiments, paper SPE 001023-G.
Leverett, M.C., and Lewis, W.B., 1941. Steady Flow of Gas-oil-water Mixtures through Unconsolidated Sands, paper SPE 941107-G.
Oak, M.J., 1990. Three-Phase Relative Permeability of Water-Wet Berea, paper SPE 20183, presented at the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma.
Pejic, D., and Maini, B.B., 2003. Three-Phase Relative Permeability of Petroleum Reservoirs, paper SPE 81021, presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad and Tobago.
Petersen, E.B., Lohne, A., Vatne, K.O., Helland, J.O., G.Virnovsky, and P.Eric Øren, 2008. Relative Permeabilities for Two- And Three Phase Flow Processes Relevant to The Depressurization of the Statfjord Field, presented at the International Symposium of the Society of Core Analysts, Abu Dhabi, UAE.
Sohrabi, M., Henderson, G.D., Tehrani, D.H., and Danesh, A., 2000. Visualisation of Oil Recovery by Water Alternating Gas (WAG) Injection Using High Pressure Micromodels - Water-Wet System, paper SPE 63000, presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas.
Sohrabi, M., Danesh, A., and Tehrani, D.H., 2005. Oil Recovery by Near-Miscible SWAG Injection, paper SPE 94073, presented at the SPE Europec/EAGE Annual Conference, Madrid, Spain.
Sohrabi, M., Tehrani, D. H. and Al-Abri, M. 2007. Performance of Near-Miscible Gas and SWAG Injection in a Mixed-Wet Core. Oral presentation of paper SCA2007-26 given at the International Symposium of the Society of Core Analysts, Calgary, 10– 12 September.
Sohrabi, M., Danesh, A., Tehrani, D., and Jamiolahmady, M., 2008. Microscopic mechanisms of oil recovery by near-miscible gas injection: Transp. Porous Media, 72, p. 351-367.
Stone, H.L., 1970. Probability Model for Estimating Three-Phase Relative Permeability, SPE Journal of Petroleum Technology, paper SPE 2116, (02).
Stone, H.L., 1973. Estimation of Three-Phase Relative Permeability and Residual Oil Data, paper SPE 73-04-06, (10-12).
Chapter 2-Coreflood Experiments
The characterization of three-phase flow in porous media and Water-Alternative-Gas injection (WAG) is a joint industrial project in Heriot-Watt University which started in 1997. The new phase of the project which has a wider scope was commenced in 2014 with the new title of “Improved Characterization of Two- and Three-Phase Flow for Reliable Reservoir Performance Prediction (Water Flooding, Gas Injection, and WAG Injection)”. A comprehensive set of coreflood experiments including two- and three-phase experiments were performed using different sandstone cores with different permeability and wettability conditions and at various gas/oil interfacial tension (IFTg/o)
values. In the new phase of the project, different cores of carbonate rocks and low permeability sandstone have been used. The experiments utilized in this research for simulation, history matching and modelling purposes were conducted by other Ph.D. students (AlAbri, M., and Fatemi, S. M.), and the present author was not involved in performing experiments and the laboratory work.
In addition to experimental data which was obtained in Heriot-Watt University, some published experimental data in the literature has been utilized by the present author. More detail will be presented accordingly. This chapter describes the coreflood facilities, rock, and fluids used at Heriot-Watt laboratory to perform unsteady state coreflood experiments.
2.1 Coreflood Facilities
A high-pressure coreflood facility is used to perform two and three-phase experiments. The coreflood rig can take long core up to 3 feet with a large diameter up to 2 inches and it is equipped with an X-ray scanner. The X-ray scanner provides scans of the core before, during, and after the experiments which can be used to monitor the fluid distribution during the flow and to check the experimental artefacts, such as capillary end effect. The rig has been designed to work at high pressures up to 6000 psia, with all components and their content being kept at a controlled temperature of 38 °C. Figure 2-1 shows a schematic diagram of this coreflood rig. In all the displacement tests, the cores are oriented horizontally and to eliminate the effect of gravity; the cores are rotating along the horizontal axis.
The coreflood rig is equipped with six pumps which are used for the injection purposes. The test fluids are maintained in stainless steel piston cells, with brine being injected into or withdrawn from the base of the cells by the displacement pumps to circulate the fluids around the flow system. To allow circulation of fluids through the core, two cells are allocated for each fluid; one is initially full, and the other is empty. A large 100 cc sight glass is placed at the core outlet. The pressure drop across the core is measured using two high accuracy transducers located at the inlet and outlet of the core. The transducers provide stable differential pressure data with an accuracy of 0.01 psi during the tests.
Figure 2-1: High-pressure coreflood facility used for displacement tests.
2.1.1 Porous Media (Cores) and Fluids
Two clean and homogenous Clashach sandstone cores with the different permeability were used for performing unsteady-state coreflood experiments. The physical properties
of these cores are given in Table 2-1. Porosity values have been measured using the Helium porosity method. The core was then saturated with 100% brine (the same brine that is utilized for the coreflood experiments), and permeability values were measured, using the brine. Before performing the coreflood tests, an X-ray scan was run, and the profile of porosity along the core was obtained. Figure 2-2 depicts the profile of the porosity along the length of the 65mD core. The average porosity from this profile is consistent for the measured porosity using Helium. Apart from some normal fluctuations in the profile, the porosity value is relatively the same along the core, which indicates that there are no major heterogeneities in the core. Both cores were chosen to be long enough to minimize the capillary end effect while performing flooding tests.
Table 2-1: Physical properties of the 65 and 1000 mD Clashach sandstone core samples.
Core Absolute
Permeability/ mD
Porosity Length/cm Diameter/cm
1 65 0.1818 60.5 5.08
2 1000 0.176 66.5 4.86
Figure 2-2: Porosity profile along the 65 mD Clashach sandstone core sample.
The pore size distribution for three Clashach sandstone core samples was examined using their mercury injection Pc curves of three samples with a broad range of
permeabilities (140, 553 and 1000 mD). Figure 2-3 shows that the Clashach sandstone shows similar pore size distribution for different permeabilities.
Figure 2-3: Pore size distribution of Clashach sandstone in a wide range of permeability.
The hydrocarbon fluid system used in the coreflood experiments was prepared from a binary mixture of methane (C1) and n-butane (nC4). The mixture has a composition of 73.6 mol% C1 and 26.4 mol% n-C4. Table 2-2 shows the measured properties of the hydrocarbon vapour (gas) and that of hydrocarbon liquid (oil), at the test temperature of 38 oC (100 ºF), and different test pressures (corresponding to different gas/oil IFT values). As the critical pressure of this hydrocarbon system at 38 oC is about 1865 psia, the test pressure of 1840 psia is very close to the critical point, and hence, the gas and oil are nearly miscible. Therefore, the test pressure of 1840 psia (which is corresponding to very low gas/oil IFT value of 0.04 mNm-1) will be considered as near-miscible conditions. At the test pressure of 1790 psia, gas/oil IFT is 0.15 mN.m-1, and this condition will be considered as intermediate IFT system, compared to the tests at a pressure of 1215 psia in which the gas/oil system will be seen as immiscible (gas/oil IFT = 2.7 mN.m-1).
Table 2-2: measured fluid properties for C1-nC4 binary mixture at 38 oC.
Pressure /psia ρg /kg.m-3 ρL /kg.m-3 µg /mPa.s µL /mPa.s IFT /mN.m-1 1215 86.68 466.06 0.0141 0.0793 2.70 1790 184.8 345.10 0.0206 0.0474 0.15 1840 211.4 317.40 0.0249 0.0405 0.04
The immobile water phase and the brine used in the experiments were synthesized with small amounts of Sodium Chloride (NaCl) and Calcium Chloride (CaCl2) dissolved in
distilled and degassed water. Table 2-3 shows the properties of the brine at 38 oC. The brine composition was designed to prevent possible adverse reaction between the brine and clay such as swelling and it was not supposed to be representative of any reservoir’s brine.
Table 2-3: Properties of synthetic brine at an experimental temperature of 38 oC.
Salinity /
mg.L-1
Density / g.L-1 Viscosity /mPa.s IFTo/w
/mN.m-1
IFTg/w
/mN.m-1
1000 992.96 0.68 55 60
To minimize the mass transfer during the coreflood experiments, all the fluids (oil, gas, and brine) were pre-equilibrated at average test pressure and temperature. They were kept in equilibrium in the high-pressure transfer vessels, which were placed in a temperature controlled oven. The mixing process was repeated several times before each displacement test to ensure that phase equilibrium conditions were satisfied.
2.1.2 Establishing Irreducible Water Saturation
Establishing immobile water saturation was a long process of sequential displacements. First, the core was fully saturated with water after being cleaned. Then, water was displaced using viscous mineral oils, and the injection continued until no further water production. The mineral oils were displaced over a period of days using decane (C10). Decane was then displaced by injecting methane (C1) at high pressure, ensuring miscible displacement. Finally, C1 was displaced by equilibrated oil (C1-nC4) at test conditions to initialize the experiment. To make sure no vaporization of the water in the core occurred during the tests, C1 and C10 were maintained in equilibrium with water before the injection. The establishment process resulted in 8% and 18% irreducible water saturation for 1000mD and 65mD cores, respectively. The profile of the established irreducible water saturation along the core was also obtained using X-ray analysis. Figure 2-4 shows irreducible water saturation (18%) profiles along the 65mD core for both water-wet and mixed-wet samples, which are very close and indicate that the established irreducible water saturations for the two wettability conditions are the same.
Figure 2-4: Established immobile water saturation along the core, obtained from X-ray for 65mD water-wet and mixed-wet cores.
2.1.3 Development of Mixed-Wettability
Core wettability can be altered by either suitable chemicals or aging in suitable crude oils. Although using chemicals for alternating the wettability is less time consuming and also has a relatively simpler procedure the stability of the wettability is poor. Aging in crude oils has a more difficult procedure and is longer. However, once the desired wettability condition has been achieved, it could be very stable and durable. A suitable crude oil was identified for wettability alteration. The procedure was tested on thin sections and small core plugs taken from the same rock before attempting to alter the wettability of the main rock. Wettability of the treated thin sections was evaluated by direct visualisation using Environmental Scanning Electron Microscope (ESEM) where the surface of thin sections was exposed to water condensation in an enclosed chamber. Figure 2-5 (a) shows a magnified picture of rock grains in a thin untreated section. Because the rock was strongly water-wet it was not possible for the condensing water to form droplets on the surface, the water would instead cover the grain surface with a spreading layer. This thin section was soaked in the crude oil and after four days, its surface was gradually exposed to water condensation. The water was observed to form droplets of varying size and contact angle on the surface which is shown in Figure 2-5 (b). This was the result of the surface being exposed to the crude oil and wettability alteration by adsorption of organic material to the grains surface (Fatemi et al. (2011)).
Figure 2-5: (a) ESEM picture for a thin section of water-wet rock: Water films were formed on the grains (b) ESEM picture for a thin section of mixed-wet rock: Water formed droplets on the grain
surfaces rather than films.
Wettability of the treated core plug was evaluated by performing a US Bureau of Mines (USBM) test (Sohrabi et al. (2007)). USBM index of (-0.02) was determined by measuring the capillary pressure curves, using the centrifuge technique. The index value shows that the core wettability was mixed-wet with an average neutral wettability.
2.1.4 Capillary Pressure Data
Figure 2-6 and Figure 2-7 show the measured air/mercury Pc for 1000 mD water-wet
core and oil/water Pc for 1093 mD mixed-wet core (obtained during USBM wettability
determination test), respectively. Currently, these are the only available measured data for Pc. The Leverett J-function (Eq.2-1) is employed to convert these Pc data for the
core and condition of interest.
cos K P J c 2-1
Pc, K,, σ and θ are capillary pressure, absolute permeability, porosity, IFT and contact
angle respectively. The similarity of their pore size distribution between two rocks is the main reason that justified use of the J-function to convert Pc data from one rock type to
another. As it was shown in Figure 2-3, the Clashach sandstone shows similar pore size distribution for a broad range of permeabilities (140, 553 and 1000 mD). It has been assumed that the 65mD Clashach sandstone core also has a similar pore size distribution.
The interfacial tension between fluids and contact angle (θ) are required to apply the J-function method. The IFT values for water/oil (58 mNm-1) and water/gas (60 mNm-1) were extracted from published measured data (Hassan et al. (1953) and Danesh (1998)).
Contact angles of 0° and 37° were assumed for the water-wet and mixed-wet core samples respectively. The converted Pc data was then used as input information in the
simulator when calculating the two-phase kr curves by history matching the coreflood
experiments.
Figure 2-6: Measured air-mercury capillary pressure for 1000 mD water-wet core.
Figure 2-7: Measured oil/water capillary pressure obtained during USBM wettability determination test carried out on 1093 mD mixed-wet core (Sohrabi et al. 2007).
2.2 Coreflood Experiments
Relative permeability is measured in the laboratory using two methods of ‘steady state’ and ‘unsteady state’ experiments. It is possible to measure relative permeability directly for a wide saturation range using the steady state method, but it is very time-consuming. In the unsteady state method or ‘displacement experiment’ for a two-phase system, the core is initially saturated with one fluid (e.g. water) then another liquid (e.g. oil) is injected into the core to displace the first fluid, at a specific rate. Injection is continued
until residual saturation of the displaced fluid is achieved. The pressure drop across the core and production data are recorded during the experiment and used to calculate relative permeabilities. The unsteady state method is less time consuming than the steady state method, but the saturation range for relative permeability is limited.
To generate a reliable source of data for fluid flow characterization and simulation purposes, a high-quality set of coreflood experiments were conducted in 65 and 1000mD water-wet and mixed-wet Clashach sandstone cores. All the two- and three-phase coreflood experiments were performed using the unsteady-state method.
The effects of different parameters such as absolute rock permeability, wettability, and gas/oil IFT values on oil recovery, the performance of gas and water alternating gas (WAG) injections and also relative permeability were investigated. These experiments include two-phase and three-phase flow systems and were performed in the presence of irreducible (connate) water saturation. The results of the unsteady-state two- and three-phase displacement tests which have been used in this thesis will be introduced in the relevant sections, and more details of experiments including total injected fluid, injection rate, and initial fluid saturations will be presented accordingly.
2.3 References
Fatemi, S. M., Sohrabi, M., Jamiolahmady, M., et al. 2011. Experimental Investigation of Near-Miscible Alternating-Gas (WAG) Injection Performance in Water-wet and Mixed-Water-wet Systems. Presented at Offshore Europe, Aberdeen, 6–8 September. SPE-145191-MS. http://dx.doi.org/10.2118/145191-MS.
Sohrabi, M., Tehrani, D. H. and Al-Abri, M. 2007. Performance of Near-Miscible Gas and SWAG Injection in a Mixed-Wet Core. Oral presentation of paper SCA2007-26 given at the International Symposium of the Society of Core Analysts, Calgary, 10– 12 September.
Chapter 3– Estimation of Three-Phase Relative Permeability (k
r) from
Unsteady-State Coreflood Experiments
The understanding of governing mechanisms of simultaneous flow of different phases (oil, water, and gas) in porous media is of great interest in petroleum and environmental engineering. In the petroleum engineering context, three-phase flow occurs in EOR processes including tertiary gas injection, water alternating gas injection (WAG), depressurization below the bubble point, gas cap expansion, solution gas drive, gravity drainage, steam injection and thermal flooding. In the environmental engineering context, three-phase flow occurs when a non-aqueous phase liquid (NAPL) or dense non-aqueous phase liquids (DNAPL) flows simultaneously with water and air through soils and also CO2 storage in geological formations.
Relative permeability (kr) is an important flow function for understanding, describing
and simulating multiphase flow through porous media. kr can be measured in the
laboratory using steady-state and unsteady-state methods, or be estimated by mathematical correlations and pore-network models. Extensive laboratory measurements and modelling were performed in two-phase flow area (Honarpour et al. (1986)), but three-phase kr did not receive similar attention. This is mainly because
three-phase flow experiments and in particular steady-state measurements are very complicated, labour intensive, time-consuming and expensive. Therefore, more often unsteady-state method as the less cumbersome method compared to the steady-state is used for three-phase kr measurements. In this chapter, the devised methodology for
3.1 Introduction
Relative permeability (kr), capillary pressure (Pc) and fluid saturations are important
macroscopic properties for describing multiphase flow through porous media. To understand multiphase flow in porous media, the relationships among these properties should be understood. These relationships are dependent on the fluids’ properties, the pore size distribution, and the saturation history and are used in diffusivity equations to describe the fluid flow in porous media.
The most common approach currently used to calculate the three-phase kr to be
employed in the numerical simulation of three-phase flow in porous media is based on available empirical correlations (models) which use laboratory-measured two-phase kr
data. These models have little or no physical basis, and the published evaluations on them (Cao & Siddiqui (2010), Delshad & Pope (1989), Baker (1988)) have demonstrated that calculating three-phase relative permeabilities by using measured two-phase kr data may lead to erroneous results. Moreover, to characterize three-phase kr and understand the effect of parameters, e.g., wettability, IFT, saturation history on flow function it is required to measure three-phase kr experimentally.
In steady state method for a two-phase system, the core is initially saturated with one fluid (e.g. water), and a specific ratio of the same fluid (water) with another fluid (e.g. oil) is injected into the core. The injection continues until the production rate for each fluid is the same as its injection rate and the pressure drop across the core is stabilized. For three-phase systems, all fluids are injected simultaneously at given ratios, until steady-state conditions are attained. It usually takes a more extended period to establish steady-state flow. Each experiment run gives one kr point only. To obtain more kr
points, the experiment is run for several different ratios of injection fluids. Using steady-state method, it is possible to calculate kr directly from Darcy’s law for a wide
saturation range, but it is very time-consuming.
In the unsteady-state method or ‘displacement experiment’ for a two-phase system, the core is initially saturated with one fluid (e.g. oil) then another fluid (e.g. water) is injected into the core to displace the first fluid, at a specific rate. Injection is continued until residual saturation of the displaced fluid is achieved. For a three-phase system, one fluid is injected to displace the other two existing fluids in the core (Figure 3-1). The pressure drop across the core and production data are recorded during the experiment and used to calculate relative permeabilities. The unsteady-state method is less time consuming than steady-state method but the saturation range for kr is limited, and its
